Finite Group Databasebeta

← #14301368

Subgroups — #14301368

Order 1920.

664 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756591C211yesmaximal, characteristic
2#11756504C211yesmaximal, characteristic, complemented
3C3×C5×#421C211yesmaximal, characteristic, complemented
4#11751337C211yesmaximal, characteristic, complemented
5#11751107C211yesmaximal, characteristic, complemented
6#11746376C211yesmaximal, characteristic, complemented
7#11746353C211yesmaximal, characteristic, complemented
8#10601210—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×#6817C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13#91836C411yescharacteristic, complemented
14#91833C411yescharacteristic, complemented
15#91829C411yescharacteristic, complemented
16#91828—22no—
17#91825C411yescharacteristic, complemented
18C4×#1220—22no—
19#91815C2211yescharacteristic
20C2×C4×Dic15C2211yescharacteristic
21C2×#6710C2211yescharacteristic
22#91796—22no—
23M16×D15—22no—
24#91790—22no—
25C3×C5×#104—22no—
26#91121—22no—
27#91090—22no—
28#70417—51nomaximal, Hall
29#66166—31no—
30#66079—31no—
31C5×#421D311yescharacteristic, complemented
32#65525—31no—
33#65295—31no—
34#64775—31no—
35#64752—31no—
36C3×C5×#41—21no—
37C3×C5×#41—21no—
38C3×C5×#41—21no—
39C3×C5×#41—21no—
40C2×C3×C5×Q8C2×C411yescharacteristic
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4C2×C411yescharacteristic
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5C2311yescharacteristic
45C2×#1220—22no—
46C2×#1220D412yes—
47C22×Dic15—21no—
48#6817—21no—
49#6817—21no—
50#6817—21no—
51#6817—21no—
52C2×D60C2×C411yescharacteristic
53C2×C4×D15D412yes—
54C2×Dic30C2×C411yescharacteristic
55C3×C5×M16—21no—
56C3×C5×M16D412yescomplemented
57C2×C3×C5×C8—21no—
58C3×C5×C4⋊C4—21no—
59C3×C5×C22⋊C4—21no—
60C3×C42×C5—21no—
61#6719—22no—
62#6719—21no—
63#6714—22no—
64C4⋊Dic15—21no—
65#6712—22no—
66C4×Dic15—21no—
67C4×Dic15—21no—
68C4×Dic15C2×C411yescharacteristic
69C4×Dic15C2×C411yescharacteristic
70#6710—21no—
71#6710D412yescomplemented
72C2×C3⋊#168—21no—
73#6705—24no—
74C8×D15—24no—
75#5832—51no—
76#5745—51no—
77C3×#421D511yescharacteristic, complemented
78#5236—51no—
79#5006—51no—
80#4555—51no—
81#4532—51no—
82C2×C5×#41C2×D311yescharacteristic
83C2×#709—31no—
84C2×C5×M16C2×D311yescharacteristic
85C5×#117C2×D311yescharacteristic
86#4093—31no—
87#4090—31no—
88#4086—31no—
89#4085—62no—
90#4082—31no—
91C4×C22⋊D5—62no—
92#4072—31no—
93C2×C4×Dic5—31no—
94C2×#681—31no—
95#4053—62no—
96D5×M16—62no—
97#4047—62no—
98C5×#104—22no—
99#3969—62no—
100#3938—62no—
101#1884—151noSylow
102C23×C3×C5—21no—
103C23×C3×C5C2×D411yescharacteristic
104C22×D15C22⋊C412yes—
105C3×C5×Q8—21no—
106C3×C5×Q8—21no—
107C3×C5×D4—21no—
108C3×C5×D4—21no—
109C3×C5×D4—41no—
110C3×C5×D4—41no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5C22×C411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5#4111yescharacteristic
120C2×C3×C4×C5#4111yescharacteristic
121#1220—22no—
122#1220—22no—
123#1220—44no—
124C2×Dic15—21no—
125C2×Dic15—21no—
126C2×Dic15—42no—
127C2×Dic15—41no—
128C2×Dic15C22⋊C412yes—
129D60—21no—
130D60—21no—
131C4×D15—22no—
132C4×D15—22no—
133Dic30—21no—
134Dic30—21no—
135C3×C5×C8—22no—
136C3⋊#168—22no—
137C2×C3×#41C2×D511yescharacteristic
138C2×#235—51no—
139C2×C3×M16C2×D511yescharacteristic
140C3×#117C2×D511yescharacteristic
141#947—51no—
142#944—51no—
143#940—51no—
144#939—102no—
145#936—51no—
146C4×#67—102no—
147#926—51no—
148C2×C4×Dic3—51no—
149C2×#208—51no—
150#907—102no—
151D3×M16—102no—
152#901—102no—
153C3×#104—22no—
154#837—102no—
155#806—102no—
156C5×#41—21no—
157C5×#41—21no—
158C5×#41—21no—
159C5×#41—21no—
160C2×C5×Q8C4×D311yescharacteristic
161C2×C5×D4—21no—
162C2×C5×D4C4×D311yescharacteristic
163C22×C4×C5—21no—
164C22×C4×C5C22×D311yescharacteristic
165C2×C22⋊D5—32no—
166C2×C22⋊D5—62no—
167C22×Dic5—61no—
168#709—61no—
169#709—61no—
170#709—61no—
171#709—61no—
172C2×D20—31no—
173C2×C4×D5—32no—
174C2×Dic10—31no—
175C5×M16—21no—
176C5×M16#6712yescomplemented
177C2×C5×C8—21no—
178C5×C4⋊C4—21no—
179C5×C22⋊C4—21no—
180C42×C5—21no—
181C22⋊Dic5—62no—
182C22⋊Dic5—61no—
183#685—62no—
184C4⋊Dic5—61no—
185#683—62no—
186C4×Dic5—31no—
187C4×Dic5—31no—
188C4×Dic5—61no—
189C4×Dic5—61no—
190#681—32no—
191#681—61no—
192C2×#168—61no—
193#676—64no—
194C8×D5—64no—
195#568—151no—
196#532—151no—
197#421—151no—
198#421D1511yescharacteristic, complemented
199#410—151no—
200#339—151no—
201#339—151no—
202C22×C3×C5—41no—
203C22×C3×C5—42no—
204C22×C3×C5—41no—
205C22×C3×C5C2×C22⋊C411yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C22×C3×C5#12111yescharacteristic
208C2×D15—22no—
209C2×D15—42no—
210C3×C4×C5—41no—
211C3×C4×C5—81no—
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12011yescharacteristic
215C3×C4×C5#12311yescharacteristic
216Dic15—22no—
217Dic15—22no—
218Dic15—41no—
219Dic15—81no—
220C3×#41—21no—
221C3×#41—21no—
222C3×#41—21no—
223C3×#41—21no—
224C2×C3×Q8C4×D511yescharacteristic
225C2×C3×D4—21no—
226C2×C3×D4C4×D511yescharacteristic
227C22×C3×C4—21no—
228C22×C3×C4C22×D511yescharacteristic
229C2×#67—52no—
230C2×#67—102no—
231C22×Dic3—101no—
232#235—101no—
233#235—101no—
234#235—101no—
235#235—101no—
236C2×D12—51no—
237C2×C4×D3—52no—
238C2×Dic6—51no—
239C3×M16—21no—
240C3×M16C22⋊D512yescomplemented
241C2×C3×C8—21no—
242C3×C4⋊C4—21no—
243C3×C22⋊C4—21no—
244C3×C42—21no—
245#217—102no—
246#217—101no—
247(C2×D3)⋊C4—102no—
248C4⋊Dic3—101no—
249Dic3⋊C4—102no—
250C4×Dic3—51no—
251C4×Dic3—51no—
252C4×Dic3—101no—
253C4×Dic3—101no—
254#208—52no—
255#208—101no—
256C2×C3⋊C8—101no—
257ΓL(1,𝔽25)—104no—
258D3×C8—104no—
259C23×C5—21no—
260C23×C5D3×D411yescharacteristic
261C22×D5—32no—
262C5×Q8—21no—
263C5×Q8—21no—
264C5×D4—21no—
265C5×D4—21no—
266C5×D4—41no—
267C5×D4—41no—
268C2×C4×C5—21no—
269C2×C4×C5—41no—
270C2×C4×C5—41no—
271C2×C4×C5—41no—
272C2×C4×C5C2×C4×D311yescharacteristic
273C2×C4×C5#23511yescharacteristic
274C2×C4×C5D3×D411yescharacteristic
275C2×C4×C5D3×D411yescharacteristic
276C2×C4×C5#23711yescharacteristic
277C2×C4×C5C2×#6711yescharacteristic
278C22⋊D5—62no—
279C22⋊D5—62no—
280C22⋊D5—124no—
281C2×Dic5—32no—
282C2×Dic5—61no—
283C2×Dic5—61no—
284C2×Dic5—122no—
285C2×Dic5—121no—
286D20—61no—
287D20—61no—
288C4×D5—62no—
289C4×D5—62no—
290Dic10—61no—
291Dic10—61no—
292C5×C8—22no—
293#168—62no—
294C2×#41—151no—
295C2×#41C2×D1511yescharacteristic
296#131—302no—
297#131—302no—
298C2×M16—151no—
299C2×M16—302no—
300C2×M16C2×D1511yescharacteristic
301C4⋊Q8—151no—
302#127—151no—
303#124—151no—
304#124—151no—
305#121—302no—
306C4×D4—302no—
307#117—151no—
308#117C2×D1511yescharacteristic
309C2×C42—151no—
310#104—22no—
311#104—302no—
312#99—302no—
313C2×C3×C5—21no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5—81no—
317C2×C3×C5#38611yescharacteristic
318D15—42no—
319C23×C3—21no—
320C23×C3D4×D511yescharacteristic
321C22×D3—52no—
322C3×Q8—21no—
323C3×Q8—21no—
324C3×D4—21no—
325C3×D4—21no—
326C3×D4—41no—
327C3×D4—41no—
328C2×C3×C4—21no—
329C2×C3×C4—41no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4C2×C4×D511yescharacteristic
333C2×C3×C4#70911yescharacteristic
334C2×C3×C4D4×D511yescharacteristic
335C2×C3×C4D4×D511yescharacteristic
336C2×C3×C4#71111yescharacteristic
337C2×C3×C4C2×C22⋊D511yescharacteristic
338#67—102no—
339#67—102no—
340#67—204no—
341C2×Dic3—52no—
342C2×Dic3—101no—
343C2×Dic3—101no—
344C2×Dic3—202no—
345C2×Dic3—201no—
346D12—101no—
347D12—101no—
348C4×D3—102no—
349C4×D3—102no—
350Dic6—101no—
351Dic6—101no—
352C3×C8—22no—
353C3⋊C8—102no—
354C22×C5—41no—
355C22×C5—42no—
356C22×C5—41no—
357C22×C5D3×C22⋊C411yescharacteristic
358C22×C5#88411yescharacteristic
359C22×C5#93811yescharacteristic
360C2×D5—62no—
361C2×D5—122no—
362C4×C5—41no—
363C4×C5—81no—
364C4×C5#67⋊C411yescharacteristic
365C4×C5#88311yescharacteristic
366C4×C5C4×#6711yescharacteristic
367C4×C5#93711yescharacteristic
368Dic5—62no—
369Dic5—62no—
370Dic5—121no—
371Dic5—241no—
372#41—21no—
373#41—21no—
374#41—21no—
375#41—21no—
376#41—301no—
377#41—301no—
378#41—301no—
379#41—301no—
380C2×Q8—151no—
381C2×Q8C4×D1511yescharacteristic
382C2×D4—21no—
383C2×D4—152no—
384C2×D4—151no—
385C2×D4—302no—
386C2×D4C4×D1511yescharacteristic
387C22×C4—21no—
388C22×C4—152no—
389C22×C4—301no—
390C22×C4C22×D1511yescharacteristic
391M16—21no—
392M16—152no—
393M16—304no—
394M16—301no—
395M16#122012yescomplemented
396C2×C8—21no—
397C2×C8—304no—
398C2×C8—301no—
399C4⋊C4—21no—
400C4⋊C4—302no—
401C4⋊C4—301no—
402C22⋊C4—21no—
403C22⋊C4—302no—
404C22⋊C4—302no—
405C22⋊C4—301no—
406C42—21no—
407C42—151no—
408C42—151no—
409C42—301no—
410C42—301no—
411C3×C5#188411yescharacteristic, complemented, Hall
412C22×C3—41no—
413C22×C3—42no—
414C22×C3—41no—
415C22×C3D5×C22⋊C411yescharacteristic
416C22×C3#403011yescharacteristic
417C22×C3#408411yescharacteristic
418C2×D3—102no—
419C2×D3—202no—
420C3×C4—41no—
421C3×C4—81no—
422C3×C4#402711yescharacteristic
423C3×C4#402911yescharacteristic
424C3×C4C4×C22⋊D511yescharacteristic
425C3×C4#408311yescharacteristic
426Dic3—102no—
427Dic3—102no—
428Dic3—201no—
429Dic3—401no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5—21no—
433C2×C5—81no—
434C2×C5#495611yescharacteristic
435D5—122no—
436C23—21no—
437C23—152no—
438C23D4×D1511yescharacteristic
439Q8—21no—
440Q8—21no—
441Q8—301no—
442Q8—301no—
443D4—21no—
444D4—21no—
445D4—41no—
446D4—41no—
447D4—302no—
448D4—302no—
449D4—301no—
450D4—301no—
451D4—604no—
452C2×C4—21no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—152no—
457C2×C4—301no—
458C2×C4—302no—
459C2×C4—302no—
460C2×C4—301no—
461C2×C4—602no—
462C2×C4—601no—
463C2×C4C2×C4×D1511yescharacteristic
464C2×C4#681711yescharacteristic
465C2×C4D4×D1511yescharacteristic
466C2×C4D4×D1511yescharacteristic
467C2×C4#681911yescharacteristic
468C2×C4C2×#122011yescharacteristic
469C8—22no—
470C8—302no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—81no—
475C2×C3#6524511yescharacteristic
476D3—202no—
477C5#7041711yescharacteristic, complemented, Sylow
478C22—41no—
479C22—42no—
480C22—41no—
481C22—302no—
482C22—602no—
483C22C22⋊C4×D1511yescharacteristic
484C22#9177311yescharacteristic
485C22#9182711yescharacteristic
486C4—41no—
487C4—81no—
488C4—302no—
489C4—302no—
490C4—601no—
491C4—1201no—
492C4#9177011yescharacteristic
493C4#9177211yescharacteristic
494C4C4×#122011yescharacteristic
495C4#9182611yescharacteristic
496C3#1060121011yescharacteristic, complemented, Sylow
497C2—21no—
498C2—21no—
499C2—21no—
500C2—81no—
501C2—602no—
502C2#1175105711yescharacteristic
subgroupG/H
centerC4#91826
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#421C2
socleC2×C3×C5#386
prime radical#11756591C2
cosocleC22×C3×C4×C5C23
hypercenter#421D15
hypocenterC3×C5#1884
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11756504C2semidirect
3. C3×C5×#421C2semidirect
4. #11751337C2semidirect
5. #11751107C2semidirect
6. #11746376C2semidirect
7. #11746353C2semidirect
13. #91836C4semidirect
14. #91833C4semidirect
15. #91829C4semidirect
17. #91825C4semidirect
31. C5×#421D3semidirect
56. C3×C5×M16D4semidirect
71. #6710D4semidirect
77. C3×#421D5semidirect
176. C5×M16#67semidirect
198. #421D15semidirect
240. C3×M16C22⋊D5semidirect
395. M16#1220semidirect
411. C3×C5#1884semidirect
477. C5#70417semidirect
496. C3#10601210semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117565912
#117565042
C3×C5×#4212
#117513372
#117511072
#117463762
#117463532
#106012103
#704175